Effective screening strategies for safe opening of universities under Omicron and Delta variants of COVID-19

As new COVID-19 variants emerge, and disease and population characteristics change, screening strategies may also need to change. We develop a decision-making model that can assist a college to determine an optimal screening strategy based on their characteristics and resources, considering COVID-19 infections/hospitalizations/deaths; peak daily hospitalizations; and the tests required. We also use this tool to generate screening guidelines for the safe opening of college campuses. Our compartmental model simulates disease spread on a hypothetical college campus under co-circulating variants with different disease dynamics, considering: (i) the heterogeneity in disease transmission and outcomes for faculty/staff and students based on vaccination status and level of natural immunity; and (ii) variant- and dose-dependent vaccine efficacy. Using the Spring 2022 academic semester as a case study, we study routine screening strategies, and find that screening the faculty/staff less frequently than the students, and/or the boosted and vaccinated less frequently than the unvaccinated, may avert a higher number of infections per test, compared to universal screening of the entire population at a common frequency. We also discuss key policy issues, including the need to revisit the mitigation objective over time, effective strategies that are informed by booster coverage, and if and when screening alone can compensate for low booster coverage.

booster in January 2022). Because the vaccinated individuals (i.e., without a booster) are assumed to receive their last dose by the start of Fall 2021 semester, we also model waning immunity.
-We model natural immunity for those individuals who have recovered from a prior infection (through the compartments, recovered & unknown, and recovered & known).
• We model population-based disparities in disease spread, hospitalization, and mortality rates to consider student versus and faculty groups, and their vaccination status. We also consider that the effectiveness of the vaccine depends on whether an individual has received the booster or not, as well as on the circulating virus variant.
• We model variant-and group-dependent disease transmission rates.
In addition, our model preserves the following features from [9]: • The test result becomes available 8 hours after taking the test. A positive test result indicates either a "false-positive," or "asymptomatic & infected;" and any subject with a positive test result moves to isolation as soon as they receive their test result. No transmission can occur during isolation. All false-positives are corrected the next day.
Both the "asymptomatic & infected" and "symptomatic & infected" subjects have an isolation time with a mean of 5 days, after which they move to the "knowingly immune" compartment, unless they are hospitalized. We assume ample isolation capacity and perfect compliance with isolation orders.
• A subject can receive natural immunity through a prior infection; this is modeled through two compartments: The subjects in the "knowingly immune" compartment have gained natural immunity through a prior asymptomatic infection that was detected during routine screening, or a prior symptomatic infection (leading to isolation in each case). The subjects in the "recovered & unknown" compartment have gained natural immunity through a prior asymptomatic infection that was undetected, thus, these subjects cannot be differentiated from "uninfected" individuals, and might get tested. We also model that individuals develop (natural) immunity throughout the semester if they have recovered from an infection. Individuals who recover from an infection are assumed to be immune for the rest of the semester. In addition, we assume that the acquired natural immunity and the immunity of the individuals who are boosted do not wane throughout the semester since the it is not long enough (80 days). Accordingly, we have 62 compartments in total, which are categorized into pools and described in detail below.
Transmission pool contains those individuals who are either susceptible, or currently infected without symptoms and with an unknown infection status (i.e., without a positive test outcome), that is, it contains the following compartments for each group i & vaccination status k: • U k,i : Uninfected and susceptible.
• A k,i : Infected and asymptomatic.
Recovered pool contains those individuals who have recovered from a prior infection (unknowingly or unknowingly), and hence developed natural immunity, and contains the following compartments for each group i and vaccination status k: • RU k,i : Recovered & unknown.
Isolation/hospital pool contains those individuals who are in isolation or at the hospital.
Accordingly, the individuals in this pool cannot transmit the infection, or if they are a falsepositive, they cannot get infected. This pool contains the following compartments for each group i & vaccination status k: • F P k,i : False-positive with no prior infection (hence in isolation).
• F P RU k,i : False-positive, and unknowingly recovered from a prior infection (hence in isolation).
• S k,i : Infected and symptomatic (hence in isolation).
Removed pool contains those individuals who have died, that is, for each group i, which are contained in the compartment, D i , Dead.
Screening pool contains those individuals who are eligible for screening based on the given screening policy.
A summary of the characteristics of each compartment is given in Table S1.

Governing Equations
The following defines the governing equations for the model depicted in Fig. S1, where

Initial Conditions
We assume a 15:1 student to faculty ratio and a medium size college campus, with a total population of 24,000 (22,500 students and 1,500 faculty members). We assume that any subject with some immunity at the beginning of the academic semester has acquired it through vaccination, but model that an individual can acquire natural immunity through an infection during the semester. We consider the following initial conditions, with multiple values for a parameter representing the values considered in sensitivity analysis: All other compartments are initially empty. Accordingly, N = 22, 500 + 1, 500 = 24, 000.
We note that for a given coverage in students, it is assumed that the coverage in faculty is 15 times less than the coverage in students. This is also assumed to be true within each vaccination status as well, i.e., whenever there is 4K unvaccinated students, it is assumed that there will be 4K/15=267 unvaccinated faculty. In this paper, we consider two options for the coverage in students: (a) 4K unvaccinated, 4K vaccinated, 14.455K boosted, and (b) 4K unvaccinated, 10K vaccinated, 8.455K boosted. This is equivalent to: (a) 82% coverage (64% boosted, 18% vaccinated) and 18% unvaccinated, and (b) 82% coverage (38% boosted, 44% vaccinated) and 18% unvaccinated. We use the latter representation in this paper and omit "18% unvaccinated for simplicity." Further, in the base case, we use the following values for X k,i , the number of imported infections per week on subjects in group i & vaccination status k if an exogenous shock takes place in that week:
In the following, we provide the detailed calculations and references for the computed parameters: • • R0 ω O (l,j) , basic reproduction number for subjects in group j & vaccination status l, for a given ω O . We assume that for j ∈ {s, f }, because, once infected, vaccinated subjects are thought to transmit COVID-19 similarly to unvaccinated subjects [10]. Then, we compute R0 ω O (u,j) as a weighted average of the respective values for the Delta and Omicron variants (see Table 3 of the Manuscript), assuming that Omicron 3 times as infectious as Delta [4,7]. As of December, 2021, the basic reproduction number for the Delta variant is reported to be between 2 and 8 [6]; and we assume that the basic reproduction number of Delta is 3.2 for the faculty and 6 for the students in the base-case transmission scenario and 2.2/5 and 4.2/7 for the faculty/students in the best-and worst-case scenarios, respectively. Then, (Table 3 of the   Manuscript).
are computed as weighted averages of the respective values for the Delta and Omicron variants, for a given ω O (see Table 3 of the Manuscript). For example, these calculations yield the following numbers for the  Table 3 of the Manuscript. in [1], to a population of subjects with different vaccination status. In particular, in time period t, the total number of susceptibles, N su (t) ≡ i k U k,i (t), hence we can write, for i, j ∈ {s, f }, l ∈ {u, v, b}: Then, β ω O (l,j),(k,i) (t) is the solution to: • π ω O (k,i) , hospitalization rate for subjects in group i & vaccination status k who are symptomatic. These rates are calculated based on hospitalization rates, denoted by H (Table   S2), and vaccine effectiveness against hospitalization in vaccinated and boosted sub- see Table S2 for values of The following include the parameters that are independent of ω O : • θ, rate at which exposed subjects become Asymptomatic & infectious: It is given by θ = 1 33.5 = 0.095 since the mean latent period is 3.5 days and each day is composed of 3 eight-hour cycles.
• σ k , rate of symptom onset in infected individuals with vaccination status k: σ k is the solution to, σ k /(σ k + ρ k ) = 30%, where 30% is the probability of developing symptoms after exposure [8], which, in the absence of reliable data, is assumed to be the same for all subjects; and ρ k is the recovery rate of infected individuals in vaccination status k, which, again in the absence of reliable data, is assumed to be the same for all subjects, and is derived from the time to recovery, assumed to be 5 days for all infected individuals [2] (independently of vaccination status and age), where each day is composed of three 8-hour cycles. Then, ρ k = 1/(3 × 5), leading to σ k = 0.0286, k ∈ {u, v, b}.
• τ k , screening rate for subjects with vaccination status k: We have, where f k is the screening frequency for vaccination status k, which can be daily, every 2 days, every 3 days, every 7 days, or every 14 days.
• γ, reduction in disease transmission rate if a face mask policy is implemented. We assume it to be γ = 0.5 based on [13].  does not include the false-positive compartments, and for those compartments that are defined for both student and faculty groups, only one compartment is shown in the figure.
Next, we enclose some results in the following tables. We note that S/S denotes screening/no screening, and u/v/b denotes unvaccinated/vaccinated/boosted vaccination status.
Thus, S u and S u,v represent strategies that customize the screening population, S u,v,b represents universal screening, and S represents no screening.